{"ID":2891737,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.16412","arxiv_id":"2507.16412","title":"Discrete-Time LQ Stochastic Two Person Nonzero Sum Difference Games With Random Coefficients:~Closed-Loop Nash Equilibrium","abstract":"This paper investigates closed-loop Nash equilibria for discrete-time linear-quadratic (LQ) stochastic nonzero-sum difference games with random coefficients. Unlike existing works, we consider randomness in both state dynamics and cost functionals, leading to a complex structure of fully coupled cross-coupled stochastic Riccati equations (CCREs). The key contributions lie in characterizing the equilibrium via state-feedback strategies derived by decoupling stochastic Hamiltonian systems governed by two symmetric CCREs-these random coefficients induce a higher-order nonlinear backward stochastic difference equation (BS$\\triangle$E) system, fundamentally differing from deterministic counterparts. Under minimal regularity conditions, we establish necessary and sufficient conditions for closed-loop Nash equilibrium existence, contingent on the regular solvability of CCREs without requiring strong assumptions. Solutions are constructed using a dynamic programming principle (DPP), linking equilibrium strategies to coupled Lyapunov-type equations. Our analysis resolves critical challenges in modeling inherent randomness and provides a unified framework for dynamic decision-making under uncertainty.","short_abstract":"This paper investigates closed-loop Nash equilibria for discrete-time linear-quadratic (LQ) stochastic nonzero-sum difference games with random coefficients. Unlike existing works, we consider randomness in both state dynamics and cost functionals, leading to a complex structure of fully coupled cross-coupled stochasti...","url_abs":"https://arxiv.org/abs/2507.16412","url_pdf":"https://arxiv.org/pdf/2507.16412v1","authors":"[\"Qingxin Meng\",\"Yiwei Wu\"]","published":"2025-07-22T10:04:26Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}